The Background of Nine Chapters of Arithmetic

Nine Chapters Arithmetic is a mathematical monograph in ancient China, and it is the most important one among the "Ten Arithmetic Classics" (ten ancient arithmetic books that appeared between Han and Tang Dynasties). Liu Hui commented on "Nine Chapters Arithmetic" in Wei and Jin Dynasties, saying: "The Duke of Zhou made a ceremony, and there were nine numbers, while nine chapters were a ceremony." He also said, "Zhang Cang, Hou Peiping in Han Dynasty, and Geng Shouchang, a senior farmer, all made good use of fortune telling. Because of the remnants of old texts, Cang and others each called it deletion and supplement, so the purpose of the school is different from ancient times or today, and the theory is closer. " According to textual research, Zhang Cang and Geng Shouchang in the Western Han Dynasty have made supplements. The final edition was written in the early Eastern Han Dynasty at the latest, but its basic content was basically finalized in the late Western Han Dynasty. There are only two kinds of mathematics books recorded in Han Shu Literature and Art Annals (written by Ban Gu according to Liu Xin's Seven Views): Xu Shang Arithmetic and Du Zhong Arithmetic, but there is no Nine Chapters Arithmetic, so it can be seen that Nine Chapters Arithmetic appeared later than Seven Views. The Biography of Ma Yuan in the Later Han Dynasty records that his grandnephew Ma Xu was "well-read and good at arithmetic in nine chapters" and was born in the last two or three decades of 1 century. According to the official names and place names in Nine Chapters Arithmetic, it can be inferred that the modern version of Nine Chapters Arithmetic was written in the second half of 1 century. "Nine Chapters Arithmetic" divides all the mathematical problems in the book into nine categories, edited by Chen.

1984, Shu Shu was unearthed in Hubei. According to textual research, it is more than a century and a half earlier than Nine Chapters of Arithmetic. Some contents in the book are very similar to Nine Chapters of Arithmetic, and some contents are basically the same. Some people speculate that the two books have a certain inheritance relationship, but there are also different views that Nine Chapters of Arithmetic has not been directly influenced by Arithmetic Book.

Most mathematicians in later generations began to study and study mathematics from the Nine Chapters of Arithmetic, and many people commented on it. The most famous ones are Liu Hui (263) and Li (656). The notes of Liu, Li and others were circulated together with Nine Chapters of Arithmetic. During the Tang and Song Dynasties, Nine Chapters Arithmetic was clearly defined as a textbook by the state. In the Northern Song Dynasty, the government also published Nine Chapters of Arithmetic (1084), which was the earliest printed mathematics book in the world. Among the modern editions of Nine Chapters Arithmetic, the earliest edition is the Southern Song Dynasty reprint of the Northern Song Dynasty (12 13), which is now in Shanghai Library (only the first five volumes are left). In Qing Dynasty, Dai Zhen copied and collated Nine Chapters of Arithmetic from Yongle Dadian. Since then, most of the editions of Sikuquanshu, Wuyingsi Rare Book and Ten Calculations inscribed by Kong (1773) are based on Dai Pai.

As a world-famous mathematical work, Nine Chapters Arithmetic was introduced to Korea and Japan during the Sui and Tang Dynasties. It has been translated into Japanese, Russian, German and French.